Exhaust Waste Heat Recovery from a Heavy-Duty Truck Engine: Experiments and Simulations

Abstract

Waste heat recovery using an (organic) Rankine cycle is an important and promising technology for improving engine efficiency and thereby reducing the CO2 emissions due to heavy-duty transport. Experiments were performed using a Rankine cycle with water for waste heat recovery from the exhaust gases of a heavy-duty Diesel engine. The experimental results were used to calibrate and validate steady-state models of the main components in the cycle: the pump, pump bypass valve, evaporator, expander, and condenser. Simulations were performed to evaluate the cycle performance over a wide range of engine operating conditions using three working fluids: water, cyclopentane, and ethanol. Additionally, cycle simulations were performed for these working fluids over a typical long haul truck driving cycle. The predicted net power output with water as the working fluid varied between 0.5 and 5.7 kW, where the optimal expander speed was dependent on the engine operating point. The net power output for simulations with cyclopentane was between 1.8 and 9.6 kW and that for ethanol was between 1.0 and 7.8 kW. Over the driving cycle, the total recovered energy was 11.2, 8.2, and 5.2 MJ for cyclopentane, ethanol, and water, respectively. These values correspond to energy recoveries of 3.4, 2.5, and 1.6 %, respectively, relative to the total energy requirement of the engine. The main contribution of this paper is the presentation of experimental data on a complete Rankine cycle-based WHR system coupled to a heavy-duty engine. These results were used to validate component models for simulations, allowing for a realistic estimation of the steady-state performance under a wide range of operating conditions for this type of system.

Full text

Exhaust waste heat recovery from a heavy-duty truck engine:
Experiments and simulations
Jelmer Rijpkema
a
,
*
, Olof Erlandsson
b
, Sven B. Andersson
a
, Karin Munch
a
a
Mechanics and Maritime Sciences, Chalmers University of Technology, Gothenburg, Sweden
b
TitanX Engine Cooling AB, S€
olvesborg, Sweden
article info
Article history:
Received 4 March 2021
Received in revised form
22 July 2021
Accepted 4 August 2021
Available online 14 August 2021
Keywords:
Experiments
Exhaust gases
Heavy-duty
Internal combustion engine
Organic rankine cycle (ORC)
Reciprocating piston expander
Long haul truck
Waste heat recovery
abstract
Waste heat recovery using an (organic) Rankine cycle is an important and promising technology for
improving engine efficiency and thereby reducing the CO
2
emissions due to heavy-duty transport. Ex-
periments were performed using a Rankine cycle with water for waste heat recovery from the exhaust
gases of a heavy-duty Diesel engine. The experimental results were used to calibrate and validate steady-
state models of the main components in the cycle: the pump, pump bypass valve, evaporator, expander,
and condenser. Simulations were performed to evaluate the cycle performance over a wide range of
engine operating conditions using three working fluids: water, cyclopentane, and ethanol. Additionally,
cycle simulations were performed for these working fluids over a typical long haul truck driving cycle.
The predicted net power output with water as the working fluid varied between 0.5 and 5.7 kW, where
the optimal expander speed was dependent on the engine operating point. The net power output for
simulations with cyclopentane was between 1.8 and 9.6 kW and that for ethanol was between 1.0 and
7.8 kW. Over the driving cycle, the total recovered energy was 11.2, 8.2, and 5.2 MJ for cyclopentane,
ethanol, and water, respectively. These values correspond to energy recoveries of 3.4, 2.5, and 1.6%,
respectively, relative tothe total energy requirement of the engine. The main contribution of this paper is
the presentation of experimental data on a complete Rankine cycle-based WHR system coupled to a
heavy-duty engine. These results were used to validate component models for simulations, allowing for a
realistic estimation of the steady-state performance under a wide range of operating conditions for this
type of system.
©2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
1. Introduction
The continuous increase of anthropogenic greenhouse gas
(GHG) emissions is causing severe adverse effects on the climate.
Consequently, the global energy system must rapidly reduce its
emissions [1]. Because heavy-duty (HD) trucks and buses are
responsible for over 5% of the total GHG emissions in Europe [2],
ways to reduce emissions from HD vehicles are needed. As a result,
the European Union has imposed CO
2
emission standards for HD
vehicles that require emission reductions of 15% from 2025 on-
wards and 30% from 2030 onwards, relative to the 2019 baseline
[3]. Several technologies and powertrain concepts have been pro-
posed to help meet these requirements, including improvements in
combustion and air management efficiency, predictive powertrain
control, hybridization, reduction of friction and other losses,
renewable fuels, hydrogen, fuel cells, and waste heat recovery
(WHR) [4,5]. WHR systems generate power from the waste heat of
the heat sources in a HD engine, namely the charge air cooler (CAC),
the exhaust recirculation (EGR) cooler, the engine coolant, or the
exhaust gases [6]. Many different WHR concepts and technologies
exist, including turbocompounding [7], thermoacoustic convertors
[8], thermoelectric generators [9], and technologies based on
thermodynamic cycles such as the Brayton [10], Stirling [11],
Rankine [12], or various flash cycles [6]. Systems based on the
(organic) Rankine cycle (ORC) have been found to achieve good
performance and flexibility, although the added weight,
complexity, and payback time remain obstacles to their commercial
implementation [13].
In an ORC-based WHR system, waste heat is used to evaporate a
working fluid at elevated pressure. The high pressure, high tem-
perature fluid is then expanded, converting the heat energy into
power, after which the fluid is condensed before entering the
*Corresponding author.
E-mail address: jelmer.rijpkema@chalmers.se (J. Rijpkema).
Contents lists available at ScienceDirect
Energy
journal homepage: www.elsevier.com/locate/energy
https://doi.org/10.1016/j.energy.2021.121698
0360-5442/©2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Energy 238 (2022) 121698

pump. The goal of the WHR system is to maximize the net power
output, while maintaining superheated vapor conditions at the
inlet of the expander [14]. The performance of such systems in
heavy-duty Diesel (HDD) engines has been the topic of many
publications (mostly simulation studies), with reported fuel savings
of over 5% [13,15]. Important issues addressed in these studies
include heat source selection [16], the choice of working fluid
[16e18], heat exchanger modeling [19,20], expander selection and
performance [21], cycle configuration [22], and techno-economic
performance optimization [23]. Due to the transient operation of
an internal combustion engine, much recent research has focused
on developing and validating dynamic models and controls for ORC
systems in HD engines [14,24e27]. In addition to the academic
interest, ORC systems for HDD engines have attracted considerable
interest from major automotive industry firms in the last decade,
including AVL [28], BMW [29,30], Bosch [31], Cummins [32,33],
Daimler [34], Honda [35], Mahle [36], Scania [37], Volkswagen [38],
Volvo Car Corporation [39,40], and Volvo Group [24,41].
A number of notable recent publications concerning experi-
mental research on WHR from HDD engines are briefly discussed
below and listed in Table 1. Seher et al. [31] reported an experi-
mental study on a Rankine cycle with water for a 12 L HDD engine.
A maximum power output of 14 kW was obtained with a piston
expander, corresponding to 4.3% of the engine power, while 9 kW
(2.8%) was achieved with a turbine expander. Based on simulations
it was concluded that water or ethanol with a piston or ethanol
with a turbine were the preferred solutions, giving a maximum
relative power of 5.3%. Furukawa et al. [42] tested two ORC systems
for WHR from a downsized HDD engine. In their first system, heat
was recovered from the engine coolant and EGR gases, reducing
fuel consumption by 3.8%. In their second system, the coolant
temperature was increased from 86 to 105

C, the exhaust gas was
included as a heat source, and a recuperator was added, improving
the fuel consumption reduction to 7.5%. Yang et al. [43] used an ORC
with R245fa and a screw expander to recover up to 28.6 kW (10.2%)
from a HDD engine. Zhang et al. [44] also used a screw expander in
an ORC with R123 for exhaust heat recovery from a HDD engine and
achieved a maximum power of 10.4 kW. Bettoja et al. [41] per-
formed experiments on two systems for two different engines: a
Volvo US10 and a CRF Cursor 11. For the Volvo engine, heat was
recovered from the exhaust and EGR with a water/ethanol mixture.
An orifice was used instead of an expander and the system was
predicted to achieve a relative power recovery between 1.5 and 3%.
For the CRF engine, a system with R245fa and a turbine was used,
giving a maximum power output of 2.5 kW. Latz et al. [45] used a
similar setup as in this paper featuring the same engine, but
recovered heat from the EGR cooler using a reciprocating piston
expander and water. The maximum recovered power in this case
was 2.7 kW. Simulations were performed to identify important
parameters for performance improvement of the EGR evaporator
and piston expander. Shu et al. [46] compared the working fluids
R123 and R245fa in a WHR system with an intermediate oil loop
connected to the exhaust of an HDD engine. No expander was
installed in the system, but, by using estimated efficiencies, a
maximum power output of 9.7 kW for R123 was predicted. In
another study, Yu et al. [47] replaced the oil loop with another
Rankine cycle with water. This improved the estimated power
output to 12.7 kW or 5.6% in relative terms. More recently, Shi et al.
[48] used the same engine for WHR from the exhaust and engine
coolant with four configurations of a CO
2
transcritical Rankine cy-
cle. Using estimated efficiencies, the maximum power output was
predicted to be 3.5 kW. Guillaume et al. [49] simulated the exhaust
conditions of a HDD engine using a boiler with thermal oil and
concluded that R1233zd(E) performed better than R245fa in their
experiments, providing a maximum power output of 2.8 kW with a
turbine expander. Alshammari et al. [50] recovered the exhaust
heat using an ORC with R1233zd(E), a turbine, and an intermediate
thermal oil loop, giving a maximum recovered power of 6.3 kW.
Their results were complemented by CFD simulations and evalua-
tions of the radial inflow turbine performance. In a more recent
study [51], the same group subsequently tested the same engine
with a WHR system featuring a thermal loop, a turbine, and
Novec649 as the working fluid. The maximum power output in this
case was 9.1 kW (11.2%). Additionally, they showed that increasing
the cooling water temperature and superheating temperature
reduced the performance of the turbine.
Although there have been many publications regarding the use
of ORC for WHR in HDD engines, there is still a lack of publicly
available experimental data. This is partly because publications
from industry often report performance improvements without
providing much detail on the cycle components. Additionally, many
publications reporting results of dynamic models often present
experimental data that was used to validate the model. These re-
sults only specify the controlled parameters (e.g. mass flow rate or
evaporator outlet temperature) without offering insight into the
cycle or component performance. In this paper, an experimental
Table 1
Recent experimental studies on WHR from HDD engines using ORCs.
Reference Year Engine Heat source Fluids(s) Expander _
W
max
_
W
max
_
W
eng
- - L/kW - - - kW %
Seher et al. [31] 2012 12.0/326 Exhaust Water Piston, Turbine 14 4.3
Furukawa et al. [42] 2014 9.0/- Exhaust, EGR, HFE Turbine e7.5
Coolant
Yang et al. [43] 2014 9.7/280 Exhaust R245fa Screw 28.6 10.2
Zhang et al. [44] 2014 -/250 Exhaust R123 Screw 10.4 4.2
Bettoja et al. [41] 2016 11.1/353 Exhaust R245fa Turbine 2.5 e
12.7/317 Exhaust, EGR Water/Ethanol ee3.0
Latz et al. [45] 2016 12.8/373 EGR Water Piston 2.7
Shu et al. [52] 2016 8.4/243 Exhaust R123, R245fa e9.7 4.0
Yu et al. [47] 2016 8.4/243 Exhaust Water, R123 e12.7 5.6
Guillaume et al. [49] 2017 -/ - Exhaust R245fa, Turbine 2.8 e
R1233zd(E)
Shi et al. [48] 2017 8.4/243 Exhaust, CO
2
e3.5 e
Coolant
Alshammari et al. [50] 2018 7.3/206 Exhaust R1233zd(E) Turbine 6.3 7.6
Alshammari et al. [51] 2019 7.3/206 Exhaust Novec649 Turbine 9.1 11.2
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
2

setup consisting of a Rankine cycle with water connected to the
exhaust of a HDD engine is evaluated and used to calibrate and
validate models of the relevant cycle components. The components
are then used to develop a realistic Rankine cycle model to deter-
mine the optimum performance in a driving cycle for a variety of
working fluids. Simulation of the driving cycle allows for an eval-
uation of the performance of the WHR system over the full oper-
ational range of the engine. However, the corresponding transient
effects are considered outside the scope of this paper, and are,
therefore, not taken into account. The goal of this publication is to
provide detailed experimental data on a full Rankine system con-
nected to a HDD engine, and to develop models that give an ac-
curate prediction of the WHR system performance under realistic
operating conditions.
2. Experimental setup
The experimental setup is shown in Fig. 1 and a schematic
overview is presented in Fig. 2. The setup consists of a heavy-duty
truck engine whose exhaust gases are used as the heat input for a
WHR system based on a Rankine cycle using water as the working
fluid. Both the engine and WHR system are placed in an engine test
cell in which the temperature and pressure can be regulated. Only
steady-state measurements are available from the engine due to
limitations on the engine brake. The setup is monitored and
controlled from the adjacent control room using multiple modules
installed in two National Instruments CompactRIO 9074 controllers
coupled to a Labview interface. Several cameras and a connecting
window allow for visual observations while running the setup.
Sensor data was measured at a sampling frequency of 10 Hz which
was written to disk every second. For each measuring point, three
minutes of data were collected and averaged.
The engine is a turbocharged 12.8 L Volvo Diesel engine with
charge air cooling (CAC) and exhaust gas recirculation (EGR); its
specifications are shown in Table 2. A Schenck D900-1e water brake
is used to control the engine speed. The engine torque is controlled
by regulating the fuel flow through manual operation of the gas
pedal. Fuel is provided from a Diesel tank located in a separate fuel
storage.
Fig. 2 shows the main components of the WHR system; their
specifications are listed in Table 3 together with the corresponding
controller where applicable. The WHR system is a typical Rankine
cycle with water as the working fluid. The suction side of the pump
is connected to the buffer tank, which is open to the atmosphere. A
controllable pump bypass valve (BPV) is installed because the flow
at the minimum pump speed would otherwise be too large to
permit full evaporation under low load engine operating condi-
tions. The evaporator uses the exhaust gases downstream the en-
gine turbocharger to evaporate and superheat the water from the
pump. It is specifically manufactured for this experimental setup by
TitanX and is shown in Fig. 3. Under start-up and shut-down con-
ditions, the fluid leaving the evaporator is not always fully evapo-
rated. Therefore, the expander inlet and outlet valves are closed and
the controllable expander bypass valve (BPV) open so the flow
bypasses the expander, preventing liquid from entering. The
expander is a reciprocating piston type with two cylinders using a
separate crankcase with its own oil circuit. Water enters the
expander as superheated steam and exits as a two-phase mixture at
low pressure. During expansion, the expander converts some of the
energy in the steam into power via an electric motor, which con-
trols the expander speed. Since some of the steam enters the
crankcase of the expander, the oil is heated to 140

C, causing this
water to evaporate and be expelled to the environment. To prevent
hot oil from entering the oil pump, the oil is subsequently cooled. In
the cycle, the oil is separated from the water and the low-pressure
two-phase mixture enters the condenser, where it is condensed
and subcooled to around 15

C using process water from the test
cell. From the condenser, the subcooled water enters the buffer
tank. To avoid overpressures in the system, safety valves (SV) are
installed on the high and low pressure sides of the cycle.
Fig. 2 also shows the locations of the different sensors in the
system; the details and accuracies are shown in Table 4. The engine
speed and torque were taken from the Schenck D900-1e mea-
surements and the fuel flow using an AVL 730 fuel balance. The
engine inlet air flow was measured using the pressure drop over a
calibrated venturi tube, sufficiently upstream the turbocharger to
avoid flow pulsations. Pressures in the system were measured using
WIKA A-10 pressure transmitters with different ranges depending
Fig. 1. Experimental setup.
Fig. 2. Schematic depiction of the experimental setup.
Table 2
Engine specifications.
Type Volvo D13 US 2010
Configuration 4 Stroke/6 Cylinder inline/EGR
Peak power 373 kW (500 hp)
Peak torque 2373 Nm
Compression ratio 16.0:1
Bore x Stroke 131 158 mm
Displacement 12.8 L
Aspiration Turbocharged
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
3

on the location. Temperature measurements were taken with 3 mm
diameter RS Pro Type K thermocouples. In the Rankine cycle, the
mass flow was measured with a coriolis mass flow meter and the
expander speed and torque were both measured with an universal
digital torque transducer.
3. Experimental results and component calibration
In this section the experimental results and modeling relations
of the main components in the WHR system are combined in
separate sections: Engine,Pump,Pump Bypass Valve,Evaporator,
Expander, and Condenser. If the results are used to calibrate and/or
validate the component, it is also shown. The last section shows the
comparison of the experiments and simulations for the full cycle
performance. A total of six different experimental sets were used, as
listed and described in Table 5, which shows the corresponding
number of experimental points and a description for each experi-
mental set.
Multiple quantities derived from the performed measurements
are presented in the subsequent sections. The standard deviations
for the measured (i.e. non-derived) data are represented by error
bars in the figures. Table 6 shows the maximum measurement error
based on the standard rules for error propagation [53].
3.1. Engine
The experimental measurements of the exhaust mass flow and
outlet temperature are shown in Figs. 4 and 5. These results are
averages based on the measurements acquired in experimental set
5 (see Table 5). The engine operating points are named in accor-
dance with the conventions of the European Stationary Cycle (ESC):
the letters A, B, and C indicate different engine speeds, and the
numbers 25, 50, 75, and 100 indicate the load percentages at the
corresponding speed [54]. An additional highway (HW) point was
tested, which represents typical engine conditions during highway
driving. These measurements were used to define the heat input
conditions used in the cycle model. The original measured mass
flows were somewhat higher than those obtained in previous
experimental studies on similar engines, suggesting that the mass
flow values measured in the test cell were systematically biased
upward. Consequently, the original mass flow values were multi-
plied by an error factor of 0.75 to obtain more realistic values. The
mass flows presented in Fig. 4 have been corrected in this manner.
3.2. Pump
The mass flow from the pump is determined from its inlet
density (
r
in
) and volume flow ( _
V
pmp
) using Eq. (1). The specifica-
tions of the pump are shown in Table 7.
_
m
pmp
¼
r
in
_
V
pmp
(1)
Although the axial piston pump is relatively insensitive to
pressure changes, the actual volume flow ( _
V
pmp
) is calculated by
applying a correction to the theoretical flow ( _
V
th
):
_
V
pmp
¼
_
V
th

_
V
corr
p
pmp;out
p
max
(2)
The theoretical flow in L/min is defined as:
_
V
th
¼V
pmp
N
pmp
(3)
The flow correction in L/min depends on the pump outlet
pressure (p
pmp, out
) in bar and the pump speed (N
pmp
) in rpm. This is
Table 3
Specifications of cycle components.
Component Brand Type Controller
Condenser Modine Plate, counter-current flow
Evaporator TitanX Plate, cross-counter flow
Expander Voith Reciprocating piston, 2-cylinder
Expander bypass valve Swagelok SS-18RS8 Integral-bonnet needle Hanbay MCL-000 AF
Expander electric motor David McClure LTD 400 V, 3-phase, 37 kW Parker DC590þIntegrator 2
Pump Danfoss PAH2 Axial piston
Pump bypass valve Swagelok SS-1RS4 Integral-bonnet needle Hanbay MCL-000 AF
Pump electric motor Hoyer HMA2 90L-4 230 V, 3-phase, 1.5 kW IMO iDrive EDX-220-21-E
Fig. 3. Exhaust evaporator.
Table 4
Measurement devices accuracy.
Input Type Range Accuracy Unit
Engine speed Schenck D900-1e 0e6500 ±2 rpm
Engine torque Schenck D900-1e 4000e4000 ±8Nm
Expander speed HBM T40B 0e20,000 ±10 rpm
Expander torque HBM T40B 500e500 ±0.25 Nm
Fuel flow AVL 730 0e150 ±0.9 kg/h
Mass flow Micro Motion F025S 0e100 ±0.2 g/s
Cycle high pressure WIKA A-10 0e60 ±0.6 bar(g)
Cycle low pressure WIKA A-10 0e6±0.06 bar(g)
Exhaust pressure WIKA A-10 0e2.5 ±0.03 bar(g)
Pressure drop Yokogawa EJA110E 0e5000 ±2.75 Pa
Temperature RS Pro Type K 75e1100 ±1.5

C
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
4

approximated in Eq. (4) using technical data from the manufacturer
[55].
_
V
corr
¼0:0001N
pmp
þ1:2 (4)
The pump power can be calculated with an estimated efficiency:
_
W
pmp
¼_
m
pmp
ðh
pmp;out
h
pmp;in
Þ.
h
pmp
(5)
To validate the pump model, measurements were conducted at
a low (set 1) and a high (set 2) pressure. In both cases, no heat was
added to the system, the pump bypass valve was fully closed, the
expander was not running, and the expander bypass valve was used
to control the pressure. The results of the experiments and simu-
lations are shown in Fig. 6, indicating that a good agreement was
achieved.
3.3. Pump bypass valve
The pump bypass valve is modeled as an incompressible flow
valve, as shown in Eq. (7). The discharge coefficient (C
d
) and valve
area (A) can be combined into an effective area (A
bpv
).
_
m
bpv
¼C
d
Affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
r
in
ðp
in
p
out
Þ
p¼A
bpv
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
r
in
ðp
in
p
out
Þ
p(6)
Although the pump bypass mass flow ( _
m
bpv
) is not known, the
evaporator mass flow ( _
m
evap
) was measured and can be subtracted
from the pump mass flow ( _
m
pmp
), available from the pump model:
_
m
bpv
¼_
m
pmp
_
m
evap
(7)
The effective area is a function of the valve position (x
bpv
) and is
calibrated using the data from experimental set 3. The calibrated
model consists of a combination of two linear functions of which
the coefficients are shown in Table 8.
The resulting effective area as a function of the valve position is
shown on the left on Fig. 7, together with the corresponding
experimental data. During these experiments no heat was added to
the system, the pump bypass valve position was controlled, the
expander was not running, and the expander bypass valve was held
at a fixed position. The corresponding results for the mass flow is
shown on the right of Fig. 7, along with results obtained under
Table 5
Numbering, quantity of experimental points (Qty.) and description of the experimental sets.
Set Qty. Description
1. 7 Cold system, no expander, low pressure, pump validation
2. 6 Cold system, no expander, high pressure, pump validation
3. 13 Cold system, no expander, pump bypass valve calibration
4. 16 Cold system, no expander, pump bypass valve validation
5. 28 Hot system, no expander, engine results, evaporator calibration, condenser results
6. 41 Hot system, expander calibration, cycle validation
Table 6
Measurement error for the derived quantities.
Quantity Symbol Max. Error
Engine mass flow _
m
eng
±5.9%
Pump power _
W
pmp
±9.4%
Bypass valve effective area A
bpv
±4.5%
Evaporator heat transfer rate _
Q
evap
±6.8%
Expander filling factor 4
f, is
±6.0%
Expander efficiency
h
exp
±8.9%
Expander power _
W
exp
±8.2%
Condenser heat transfer rate _
Q
cond
±7.9%
Fig. 4. Engine speed-torque map showing the measured engine exhaust mass flow.
The measurements were corrected by a factor 0.75 based on an estimated error of the
measured values.
Fig. 5. Engine speed-torque map showing the measured engine exhaust outlet
temperature.
Table 7
Pump specifications [55].
Maximum pressure p
max
100 bar
Displacement volume V
pmp
0.002 L
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
5

different conditions (set 4) that were used for model validation.
Good agreement with the experiments is observed for both for the
calibration and validation data sets.
3.4. Evaporator
The exhaust evaporator is a cross-counter flow plate heat
exchanger with fins; its heat transfer area is depicted schematically
in Fig. 8. The exhaust flow side has one pass and 36 channels, while
the water side has three passes and 35 channels. The dimensions of
the heat exchanger are listed in Tables 9 and 10. The model only
accounts for heat transfer; the pressure drop over the evaporator is
ignored.
Heat transfer is modeled using fin-specific equations. The geo-
metric parameters of the fins are computed using the values pre-
sented in Table 10 and the following equations [56]:
D
h
¼4s
f
bL
f
2ðs
f
L
f
þbL
f
þt
f
bÞþt
f
s
f
(8)
A
flow
¼s
f
h
f
(9)
A
base
¼2ðs
f
L
f
þt
f
ðs
f
t
f
Þ.2Þ(10)
A
fin
¼2ðh
f
L
f
þh
f
t
f
Þ(11)
For each pass and channel the number of fins for the working
fluid and exhaust can be calculated:
n
f;x;wf
¼L
p
f
;n
f;y;wf
¼H
L
f
(12)
n
f;x;exh
¼L
L
f
;n
f;y;exh
¼H
p
f
(13)
As a result, the total cross-sectional area (or total flow area) for
the flow can be calculated:
Fig. 6. The mass flow as a function of the pump speed and pump outlet pressure.
Table 8
Pump bypass valve coefficients.
x
bpv
% 0 1 2 7 100
A
bpv
mm
2
0 0.25 0.35 1 2.65
Fig. 7. Pump bypass valve effective area (left) and mass flow (right) as a function of the bypass valve position.
Fig. 8. Schematic depiction of the heat transfer area of the exhaust evaporator.
Table 9
Heat exchanger dimensions.
Heat exchanger length L144 mm
Heat exchanger width W241 mm
Heat exchanger height H247 mm
Channel height b3.00 mm
Plate thickness t0.40 mm
Fluid-specific wf exh
Number of channels n
ch
35 36 e
Number of passes n
pass
31 e
Number of fins in x-dir. n
f, x
96.0 45.4 e
Number of fins in y-dir. n
f, y
77.8 164.7 e
Number of fins n
f
7468 7468 e
Total flow area A
c
4309 22,808 mm
2
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
6

A
c;wf
¼n
ch;wf
n
f;x;wf
n
pass;wf
A
flow
(14)
A
c;exh
¼n
ch;exh
n
f;y;exh
n
pass;exh
A
flow
(15)
The mass flux (G) for the exhaust and water sides is calculated
by dividing the mass flow by the corresponding cross-sectional
area (G¼_
m=A
c
). With these definitions and the associated ther-
modynamic and transport properties, the Reynolds number (Re),
the Prandtl number (Pr), and the heat transfer coefficient (
a
) can be
determined using the Nusselt (Nu) number. For single-phase heat
transfer, the following expression for the Nusselt number [56]is
used:
Nu ¼jRePr
1=3
(16)
Where:
j¼0:652Re
0:540
s
f
h
f
!
0:154
t
f
L
f
!
0:150
t
f
s
f
!
0:068
,2
41þ5:269,10
5
Re
1:34
s
f
h
f
!
0:504
t
f
L
f
!
0:456
t
f
s
f
!
1:06
3
5
0:1
(17)
The two-phase heat transfer coefficient is the sum of the
nucleate boiling (
a
nb
) and convective (
a
cv
) components [56]:
a
¼
a
nb
þ
a
cv
(18)
The nucleate boiling component is a function of the heat flux ( _
q)
for each element, the molecular weight (M
w
), and the reduced
pressure (p
crit
), and is defined as:
a
nb
¼55_
q
2=3
M
1=2
w
p
p
crit

0:225
log
10
p
p
crit

0:55
(19)
The convective component is obtained from the saturated liquid
heat transfer coefficient (
a
l
), which is computed using Eq. (16) with
saturated liquid properties. This coefficient is then multiplied by a
factor (F) that depends on the steam quality (x) and the saturated
liquid and vapor densities (
r
l
,
r
v
) and viscosities (
m
l
,
m
v
):
a
cv
¼F
a
l
(20)
F¼1þ28
X
tt

0:372
(21)
X
tt
¼1x
x
0:9

r
v
r
l

0:5

m
v
m
l

0:1
(22)
To solve the heat transfer equations, the heat exchanger is dis-
cretized into a set of elements as shown in Fig. 9. A low resolution
model is compared to a high resolution TitanX model whose set-
tings are shown in Table 11. The heat transfer surface (A
s
) is the
combined base (A
base
) and fin(A
fin
) surface:
A
s;el
¼A
base;el
þA
fin;el
(23)
The heat transfer is calculated for all channels based on the total
surface area for each element:
A
s;el;tot
¼n
ch;wf
A
s;el
(24)
For each element the heat transfer can be calculated:
_
Q
el
¼U
el
A
s;el;tot
ðT
exh;el
T
wf;el
Þ(25)
The overall heat transfer coefficient (U) consists of the sum of
the separate contributions:
1
U¼1
a
wf
þt
w
l
w
þ1
a
exh
z1
a
wf
þ1
a
exh
(26)
The experimental and simulation results of the evaporator heat
transfer rate and outlet temperature are shown in Fig. 10, based on
experimental set 5 from Table 5. Experiments were performed at
every engine operating point shown in Figs. 4 and 5 (A25-C100). In
these experiments, the pump and pump bypass valve position were
controlled to maintain a constant mass flow at each operating
point. The expander was not running and the expander bypass
valve was used to control the pressure. Both the low resolution
model and the TitanX model exhibit good agreement with the
experiments. However, it should be noted that in most cases the
available heat from the exhaust gases was so large that the water
was superheated to a temperature close to the exhaust gas inlet
temperature. Increasing the mass flow would reduce the evapo-
rator outlet temperature of the water, but the magnitude was
difficult to control experimentally. Because of the relatively small
mass flows and high latent heat of water, small deviations in mass
flow caused large deviations in the evaporator outlet temperature.
Another possible source of error is that the temperatures were
measured at a single location, slightly downstream of the evapo-
rator outlet. This could cause variations between the experimental
values due to heat loss and local effects, leading to deviations from
the model values. However, since the heat transfer to the working
fluid is the most important for the prediction of the cycle perfor-
mance, the model can still be used in the cycle simulations.
Table 10
Fin geometry.
Spacing s
f
1.35 mm
Thickness t
f
0.15 mm
Strip flow length L
f
3.175 mm
Pitch p
f
1.50 mm
Effective channel height h
f
2.85 mm
Hydraulic diameter D
h
1.791 mm
Flow area A
flow
3.848 mm
2
Base area A
base
8.753 mm
2
Fin area A
fin
18.95 mm
2
Fig. 9. Discretization of the exhaust evaporator.
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
7

3.5. Expander
The expander is an uniflow reciprocating piston expander with
two cylinders of which the relevant geometrical specifications are
shown in Table 12.
The expander model is based on a semi-empirical model for
volumetric expanders [57] which is schematically shown in Fig. 11.
The semi-empirical model consists of thermodynamic equations
with tuning parameters that are determined by calibrating them
against experimental results. Using these parameters, the de-
viations from ideal expander performance caused by pressure
drops, leakage, heat losses, and mechanical losses can be deter-
mined. More details on the modeling, results, and validation of the
expander were presented in a previous publication [58].
The operation of the expander is characterized by three main
performance factors: the isentropic filling factor (4
f, is
), the
expander efficiency (
h
exp
), and the isentropic effectiveness (ε
is
). All
three factors depend on the process conditions and expander
operation. The isentropic filling factor (4
f, is
) is used to predict how
much the expander mass flow will deviate from ideal conditions
under isentropic outlet conditions. For a piston expander, the
theoretical flow is equal to product of the expander speed (N
exp
)
and the difference between the available mass at inlet valve closing
(
r
exp, in
f
a
V
exp
) and the trapped mass at exhaust valve closing (
r
exp,
out
f
p
V
exp
). In all tested conditions, the expansion ended in the two-
phase region. Therefore, the outlet conditions are based on the
isentropic conditions (
r
exp, out, is
f
p
V
exp
). This leads to the following
expression:
_
m
exp
¼
r
exp;in
f
a

r
exp;out;is
f
p
4
f;is
V
exp
N
exp
60 (27)
To predict the shaft power output of the expander ( _
W
exp
), the
expander efficiency is used:
_
W
exp
¼
h
exp
_
m
exp
ðh
exp;in
h
exp;out;is
Þ(28)
For the expander considered in this paper, not only the shaft
power output, but also the leakage and heat loss effects were sig-
nificant. Therefore, the isentropic effectiveness (ε
is
) is introduced,
which is used to calculate the expander outlet enthalpy:
h
exp;out
¼h
exp;in
ε
is
ðh
exp;in
h
exp;out;is
Þ(29)
The resulting model outputs and the corresponding experi-
mental values are shown on the left of Figs. 12 and 13, taken from
experimental set 6. Experiments were performed at four engine
operating points (A25, HW, A50, and B25). In the experiments, the
pump and pump bypass valve position were controlled to provide a
constant mass flow at each engine operating point, the expander
speed was varied, and the expander bypass valve was closed. The
results show that the expander mass flow is well captured by the
isentropic filling factor. However, the shaft power is overpredicted
for low pressure ratios (and corresponding low power outputs) and
underpredicted at higher pressure ratios (and corresponding high
power outputs). Since the expander efficiency is not only depen-
dent on the pressure ratio, variations between experimental values
for similar pressure ratios occur. Other important physical quanti-
ties include the expander speed, the cycle mass flow, and the
expander inlet temperature. Deviations between model and
experimental values are mainly attributed to the expansion in the
two-phase region, high leakage rate in the expander, and the
change in lubrication properties over time. These topics are dis-
cussed in more detail in a separate publication [58].
3.6. Condenser
The condenser is modeled as a heat sink only because neither
detailed information on its geometry nor flow measurements on
Table 11
Heat exchanger geometry for each element.
Model TitanX
Number of els. in x-dir. n
el, x
69e
Number of els. in y-dir. n
el, y
310e
Number of fins n
f, el
415 83 e
Base area A
base, el
3631 726 mm
2
Fin area A
fin, el
7864 1573 mm
2
Heat transfer area A
s, el
11,495 2299 mm
2
Fig. 10. Evaporator heat transfer rate (left) and outlet temperature (right) as a function of the mass flow.
Table 12
Expander specifications.
Supply cut-off f
a
0.16 e
Exhaust cut-off f
p
0.78 e
Displaced volume V
exp
0.8 L
Fig. 11. Schematic depiction of the semi-empirical model used for the expander [58].
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
8

the process water used for cooling were available. Assuming no
leakage of the working fluid, the modeled condenser flow was
considered to be equal to the evaporator flow. This gives the
following relations for the condenser:
_
m
cond
¼_
m
evap
(30)
_
Q
cond
¼_
m
cond
ðh
cond;out
h
cond;in
Þ(31)
Fig. 14 shows the experimental results of the condenser heat
transfer rate from experimental set 5 in Table 5 together with the
corresponding outlet temperatures. Experiments were performed
at all of the engine operating points shown in Figs. 4 and 5 (A25-
C100). In these experiments, the pump and pump bypass valve
position were controlled to provide a constant mass flow at each
engine operating point. The expander was not running and the
expander bypass valve was used to control the pressure.
3.7. Rankine cycle
Simulations using the full cycle model incorporating all of the
calibrated component models discussed in the preceding sections
were performed in MATLAB [59] using fluid maps generated from
the CoolProP [60] database. Fig. 15 shows the comparison of these
simulation results to data from experiment set 6 in Table 5. Ex-
periments were performed at four engine operating points (A25,
HW, A50, and B25). The pump speed and pump bypass valve po-
sition were controlled to provide a constant mass flow, the
expander speed was varied, and the expander bypass valve was
closed.
The comparison of the model output to the experimental values
shows that the pump outlet pressure is well captured. Deviations in
the mass flow are mostly due to the sensitivity of the pump bypass
valve model; small pressure changes cause large changes in the
predicted flow through the bypass valve, leading to poor agreement
between the model and experiment. Because the evaporator heat
Fig. 12. The isentropic filling factor (left) and mass flow (right) of the expander as functions of the expander speed. Symbols indicate experimental results and lines indicate model
outputs.
Fig. 13. The efficiency (left) and shaft power (right) of the expander as functions of the expander speed. Symbols indicate experimental results and lines indicate model outputs.
Fig. 14. Condenser heat transfer rate (left) and outlet temperature (right) as functions of the mass flow.
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
9

transfer rate is proportional to the mass flow, the same effect is
visible there. Also visible is the overprediction of the evaporator
outlet temperature. Since no heat loss was considered in the
models, the evaporator outlet temperatures of the working fluid
almost reached the exhaust gas temperature. In reality, heat losses
would lead to slightly lower temperature, explaining the deviations
between simulations and experiments. Finally, the expander
output power is significantly overpredicted at low power outputs
and underpredicted at higher power outputs; the reasons for this
are discussed in more detail in a separate publication [58].
The main source of error between the experimental and simu-
lated values of the mass flow is the bypass valve model. A smaller
pump in the experimental setup would possibly eliminate the need
for a bypass valve. Alternatively, a more sophisticated model or
calibration method for the bypass valve could improve the fit be-
tween experiments and simulations. Using a different working fluid
could also help improve the fit. A fluid with a smaller latent heat
would mean higher mass flows to extract the available heat.
Simultaneously, the calibration and validation for the heat
exchanger and the expander models could be improved. Another
improvement would be the addition of pressure drop and heat loss
correlations to the models. Although the figures show that the
deviations between simulation and experimental results can be
significant, the simulation results are based on physical models and
the general trend is well-captured. This means that these models
are a valid tool to compare the performance of different working
fluids for operational range of the engine, which is done in the
subsequent sections.
4. Simulation setup
The validated cycle model allows for predicting the performance
of the WHR system under conditions outside the experimentally
tested range (e.g. over a driving cycle) and with different working
fluids. For this purpose, the bypass valve is removed from the
original model, giving the cycle schematically depicted in Fig. 13.To
obtain the desired mass flow, the pump is allowed to operate at
speeds outside the range specified by the manufacturer.
4.1. Working fluids
To evaluate the performance of the WHR system, simulations
were performed with two additional working fluids: cyclopentane
and ethanol. These fluids were selected based on their promising
thermodynamic performance in heavy-duty engine applications
[17,61]. Previous studies by the authors [6,16,62], where different
heat sources from the engine were evaluated for many different
working fluids, also showed good thermodynamic performance for
these two fluids. Additionally, they are environmentally friendly,
relatively non-toxic, and non-corrosive, although flammability is a
concern for both of them. Table 13 lists a number of important
properties for the three working fluids.
4.2. Driving cycle
The model was calibrated against experimental data obtained in
an engine test cell. However, temperatures under driving condi-
tions are usually lower due thermal inertia and heat loss in the
aftertreatment systems and exhaust piping. Therefore, the input
conditions for the simulations were taken from a representative
driving cycle for a 40 tonne EU6 Scania long haul truck driving on a
European road. The vehicle speeds and road gradients for this
driving cycle are shown in Fig. 16.
The exhaust outlet conditions (temperature and mass flow)
during the driving cycle are divided into a four-by-four grid, as
Fig. 15. Comparison of full cycle model outputs and experimental results.
Table 13
Properties of the selected working fluid.
Fluid MW p
crit
T
crit
GWP ODP Type
- kg/kmol bar

C-
Cyclopentane 70.1 45.7 239 0 0 isentropic
Ethanol 46.1 62.7 240 0 0 wet
Water 18.0 220 374 0 0 wet
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
10

shown in Fig. 18. The percentages in the grid represent the relative
duration of these conditions during the driving cycle. The green
values indicate the duration for a positive torque on the engine and
the red values indicate negative torque. The center points for all 16
elements were used as inputs for the steady-state simulations.
Transient effects during the driving cycle were not taken into
account.
4.3. Cycle performance
To run the simulations, a number of inputs and constraints were
specified, as summarized in Table 14. The exhaust mass flow,
temperature, and pressure were taken from the 16 previously
defined operating conditions. Depending on whether the engine
torque was positive or negative, the expander was coupled directly
to the engine via a mechanical coupling or to an electrical gener-
ator. A subcooling temperature difference of 5 K was set to prevent
vapor entering the pump. The pump mechanical efficiency, elec-
trical generator efficiency, and the efficiency of the mechanical
coupling between expander and engine were taken to be 0.50, 0.85,
and 0.98, respectively. Only subcritical conditions were taken into
account. The evaporator outlet temperature was limited to avoid
thermal instability of the working fluid and overheating of sus-
pended oil. To allow for temperature control, a minimum and
maximum superheating temperature difference were set. The
range of expander speeds was based on the specifications from the
manufacturer [63]. The pump speed was not limited by these
specifications; instead it was set to give the highest possible mass
flow. No pressure drops in the components were considered and
component heat losses other than the expander heat loss were
ignored. A golden section search was performed to find the
expander speed providing the maximum power output for the
stated inputs and constraints.
Cycle performance is evaluated based on the net (shaft) power
and thermodynamic efficiency:
_
W
net
¼
_
W
exp

_
W
pmp
(32)
h
th
¼
_
W
net
_
Q
evap
(33)
The performance in the driving cycle is estimated using the
definitions expressed in Eqs. (34) and (35). At positive engine tor-
que (
t
eng
), the expander power is directly provided to the engine,
while at negative engine torque the expander power is converted
into electrical power.
_
W
pmp;el
¼
_
W
pmp
h
el
(34)
_
W
exp
¼(_
W
exp;mech
¼
h
mech
_
W
exp
;if
t
eng
>0
_
W
exp;el
¼
h
el
_
W
exp
;if
t
eng
0(35)
5. Results and discussion
5.1. Steady-state performance
Steady-state simulations using the cycle model with water as
the working fluid were performed for 16 engine operating points
with exhaust mass flows ( _
m
exh
) ranging from 150 to 450 g/s and
exhaust outlet temperatures (T
exh, out
) between 260 and 320

C, as
previously presented in Fig. 18 and Table 14. In the following dis-
cussion, these will be designated with an M for mass flow and a T
for temperature. Thus, M150T300 corresponds to an exhaust mass
flow of 150 g/s and an outlet temperature of 300

C. The pump
Fig. 16. Schematic of full cycle model.
Fig. 17. Representative driving cycle for a long haul truck on an European road.
Fig. 18. Relative time distributions of the exhaust mass flow and temperature over the
driving cycle. Green values indicate positive torque and red negative torque. The total
drive cycle duration (
D
t
dc
) is 2748 s. (For interpretation of the references to colour in
this figure legend, the reader is referred to the Web version of this article.)
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
11

outlet pressures and mass flows at four engine operating points for
a range of expander speeds are shown in Fig. 19. In these cases, the
evaporator superheating temperature difference was kept within
the constraints specified in Table 14. At each engine operating
point, the exhaust temperature was kept constant while varying
the mass flow, effectively changing the heat available for recovery.
As expected, the pump outlet pressure decreased as the
expander speed increased and increased as the available exhaust
heat increased (represented by the engine operating points). An
increase in the available exhaust heat allows for higher cycle mass
flows, as shown on the right of Fig. 19. The same effect was
observed when increasing the expander speed. Increasing the
expander speed (and thus reducing the evaporating pressure of
water in the cycle, as explained further on; see Fig. 22) made it
possible to recover more heat from the exhaust gases. The resulting
net power, shown on the left of Fig. 20, depends on the required
pump power, the amount of heat transferred from the heat source,
and the expander power obtained. The pump power is determined
by the pump efficiency, the pressure difference over the pump,and
the mass flow. The amount of heat transferred from the source to
the cycle is a function of the exhaust mass flow and temperature, as
well as the cycle temperature, pressure, and mass flow. The
expander power depends on how effectively the recovered heat is
transformed into power, which is shown on the right of Fig. 20.
Because of the interaction between the pump power, recovered
heat, and expander power, there is no single optimal expander
speed that maximizes the power output for all engine operating
points. For the lower exhaust mass flows, the maximum net power
is around 1.1 kWand is achieved at a relatively low expander speed
of around 900 rpm. As the exhaust mass flow increases, both the
power output and the optimal expander speed increase, with
maxima of 4.2 kW and 2800 rpm, respectively.
Simulations were performed to obtain the maximum power
output for the 16 engine operating points with water as the
working fluid. The expander speed was varied at each operating
point to obtain the maximum net power output, which is shown on
the left of Fig. 21. The values shown at the edges of this figure were
obtained by linear extrapolation. Depending on the exhaust mass
flow and temperature, the recoverable net power ranges from 0 to
8 kW. Another important aspect for automotive applications is the
amount of heat that must be rejected to allow condensation of the
working fluid, which is shown on the right of Fig. 21. When using
exhaust gases as a heat source, this heat must be either transferred
to the coolant and rejected in the coolant radiator or rejected
directly via a separate radiator. The results of the simulations show
that the heat transfer rate in the condenser can be as high as 60 kW.
Simulations using the same cycle components were also per-
formed with cyclopentane and ethanol as the working fluid, and
the results all selected working fluids are shown in Table 15. The
condensation pressure was set at 1.1 bar for all fluids, resulting in a
different condensation temperature for each fluid. A lower
condensation temperature means a smaller temperature difference
between the working fluid and the ambient temperature, making it
more difficult to reject excess heat. In a practical system, this could
lead to increased power consumption by the cooling fan, which
would reduce the net power output of the system. This effect is not
taken into account here.
The results from Table 15 show that the highest power output
was obtained with cyclopentane, then ethanol, and finally water.
These differences in the performance can be explained by consid-
ering the M150T300 engine operating point, for which the results
are shown in Table 16.
The power outputs for cyclopentane and ethanol were higher
than for water because of higher mass flows and expander
Table 14
Cycle inputs and constraints.
Inputs
Exhaust gas mass flow _
m
exh
150e450 g/s
Exhaust gas inlet temperature T
exh, in
260e320

C
Exhaust gas inlet pressure p
exh, in
1.03e1.06 bar
Pump inlet subcooling temperature
D
T
sub
5K
Pump mechanical efficiency
h
pmp
0.50 e
Electrical generator efficiency
h
el
0.85 e
Mechanical coupling efficiency
h
mech
0.98 e
Constraints
Pump outlet pressure p
pmp, out
10 ep
crit
bar
Evaporator outlet temperature T
evap, out
n/a e260

C
Evaporator outlet superheating temp.
D
T
sup
10e30 K
Expander speed N
exp
500e3500 rpm
Pump speed N
pmp
150e6000 rpm
Fig. 19. Pump outlet pressure (left) and mass flow rate (right) for water as functions of the expander speed at different engine operating points.
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
12

efficiencies. The higher mass flows of cyclopentane and ethanol are
due to the lower latent heat of these fluids and to a better thermal
match between the heat source and the cycle. This is visualized in
the heat transfer-temperature (QT) diagrams for the different
working fluids at the M150T300 engine operating point, which are
presented in Fig. 22. For cyclopentane, the temperature slope dur-
ing preheating matches the temperature profile of the heat source,
meaning that the heat transfer is not limited by the evaporating
temperature of the working fluid and the maximum heat can be
extracted for this specific heat exchanger geometry. For ethanol and
especially for water, less heat can be extracted and a lower power
output is achieved.
The corresponding temperature-entropy (Ts) diagrams are
shown in Fig. 23. This shows that the expansion ends in the two-
phase region in the cases of ethanol and water whereas for cyclo-
pentane it ends in the superheated region. For most expanders,
Fig. 20. Net shaft power (left) and expander efficiency (right) for water as functions of the expander speed at different engine operating points.
Fig. 21. Net shaft power (left) and condenser heat transfer rate (right) for water as a function of the exhaust mass flow and temperature. The values at the edges were linearly
extrapolated.
Fig. 22. QT-diagrams of cyclopentane, ethanol, and water for the M150T300 engine operating point.
Table 15
Range of cycle conditions for the 16 engine operating points.
Fluid _
m
pmp
p
evap
T
exp, in
N
exp
p
cond
T
cond
_
Q
cond
_
W
net
h
th
- g/s bar

C rpm bar

CkW kW %
Cyclopent. 38.6e142 19.4e30.9 194e225 1285e3500 1.1 52 17.4e75.0 1.8e9.6 7.7e11
Ethanol 18.6e74.4 20.9e30.1 193e232 861e2774 1.1 80 14.6e66.3 1.0e7.8 5.9e9.8
Water 5.16e22.6 15.1e26.5 210e255 700e3139 1.1 102 10.2e45.8 0.5e5.7 3.7e10
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
13

operation in the superheated region is preferable because it pre-
vents droplets from damaging the expander. Additionally, when
using cyclopentane, a recuperator could be added to improve the
power output or reduce the condenser load. Although the Ts-
diagrams suggest that the expander is operating at isentropic effi-
ciency, this is not the case. During the expansion, not all of the
available energy is converted to power; a significant portion is lost
as heat, which is why two definitions for the expander power and
energy change are necessary, as defined in Eq. (28) and Eq. (29).
5.2. Driving cycle performance
The exhaust flow and temperature over the driving cycle pre-
sented in Fig. 17 were used as inputs for the steady-state simula-
tions of the three selected working fluids. The resulting net power
outputs over the driving cycle of these fluids are shown in Fig. 24.
In accordance with the steady-state simulations, the best per-
formance was obtained with cyclopentane, followed by ethanol and
then water. To estimate performance over the whole driving cycle,
the results were numerically integrated using a timestep (
D
t)of1s:
W¼X
n
i¼1
_
W
i
D
t(36)
The integrated results for Eqs. (31), (34) and (35) are shown in
Table 17, both in absolute and relative terms. The relative perfor-
mance is obtained by dividing the absolute result by the total work
done by the engine during the driving cycle (W
dc
¼333 MJ). The
results show that the WHR system can recover a significant amount
of energy, corresponding to as much as 3.37% of the total engine
energy requirement. This relative recovery can be roughly trans-
lated into fuel consumption reduction, assuming that the increased
backpressure due to the exhaust evaporator does not affect the
engine efficiency. The results also show that the recovered elec-
trical work is comparable to the electrical work done by the pump,
although it must be noted that the efficiencies of storing and
extracting power from the battery are not included. Additionally,
the table shows that the pump work is much higher for cyclo-
pentane than for the other fluids because of the higher mass flow in
the cycle. However, this is more than offset by the increase in
expander power.
Even though a driving cycle was used to evaluate the perfor-
mance of the working fluids over the operational range of the en-
gine during actual driving conditions, transient effects were
ignored in this paper. The cycle components are assumed to react
instantaneously to changes in the exhaust flow and temperature. In
reality, the performance of the components will be affected by
inertia during transient operation, with the thermal inertia in the
heat exchangers being dominant [64]. This has important impli-
cations for the control of the system, as superheated conditions at
the inlet of the expander should be ensured [14]. Another study
[65] showed in a comparison between a steady state and transient
model that a transient model will lead to lower fuel savings,
although the resulting ranking remains the same. The expander
coupling is another point of discussion. If the expander is me-
chanically coupled to the engine, its speed will be determined by
Table 16
Cycle conditions for the M150T300 engine operating point.
Fluid _
m
pmp
p
evap
T
exp, in
N
exp
p
cond
T
cond
_
Q
cond
_
W
net
h
th
- g/s bar

C rpm bar

CkWkW%
Cyclopentane 52.9 21.6 199 1546 1.1 52 27.7 2.75 8.7
Ethanol 25.2 23.4 214 1023 1.1 80 20.9 1.81 6.9
Water 7.45 18.7 228 1023 1.1 102 14.7 1.09 6.0
Fig. 23. Ts-diagrams of cyclopentane, ethanol, and water at the M150T300 engine operating point.
Fig. 24. Net shaft power for multiple fluids during the driving cycle.
Table 17
Driving cycle performance with a total engine work requirement of 333 MJ.
Fluid Q
cond
W
pmp, el
W
exp, mech
W
exp, el
W
*
net
MJ MJ (%) MJ (%) MJ (%) MJ (%)
Cyclopentane 100 1.62 (0.49) 11.7 (3.50) 1.17 (0.35) 11.2 (3.37)
Ethanol 86.1 0.90 (0.27) 8.42 (2.53) 0.69 (0.21) 8.21 (2.46)
Water 57.1 0.20 (0.06) 5.02 (1.51) 0.37 (0.11) 5.19 (1.56)
*W
net
¼W
exp, mech
þW
exp, el
W
pmp, el
.
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
14

the engine speed and a predetermined gear ratio. However, the
driving cycle results presented here were obtained under the
assumption that the expander could operate at its optimal speed for
which the corresponding power output were determined in the
earlier steady-state simulations. The results in this section allow for
comparison of different working fluids on the basis of their ther-
modynamic performance. In practice, however, the selection of the
best working fluid is also subject to other constraints such as costs,
component sizing, and environmental impact.
6. Conclusions
Experimental investigations were performed to evaluate the
performance of a Rankine system with water for WHR from the
exhaust gases of a heavy-duty engine. The results of these experi-
ments constitute one of the main contributions of this paper.
Additionally, models of the relevant cycle components were
developed and then calibrated and validated against the experi-
mental data. These models provided more detailed overview of the
physical processes occurring within each component. This allowed
for predictions of the performance of these components under
conditions outside the experimental range and when using
different working fluids. The component models were combined to
create model of the full cycle, allowing the performance of the
Rankine system to be simulated over a typical long haul truck
driving cycle. The main results and conclusions obtained during
this work were:
CExperimental results were obtained for a wide range of en-
gine operating conditions. The experiments were divided
into six distinct experimental sets and their results were
used to calibrate and validate models of the main compo-
nents of the Rankine cycle, i.e. the pump, pump bypass valve,
evaporator, expander, and condenser. Experimental mea-
surements of the expander shaft power were performed at
four different engine operating points (A25, HW, A50, B25).
The expander power ranged from 0.2 to 3 kW, corresponding
to 0.2e2.5% of the engine power.
CSteady-state simulations of the Rankine cycle with water as
the working fluid exhibited good agreement with the
experimentally determined mass flow and evaporator heat
transfer, but the expander power was overpredicted at low
expander powers and underpredicted at high powers. Sim-
ulations performed at 16 engine operating points gave net
power outputs between 0.5 and 5.7 kW, and the optimal
expander speed was found to be dependent on the engine
operating point. The added heat needing to be rejected in the
condenser was between 10 and 46 kW. These values can be
extrapolated to obtain results for the full range of operating
conditions, yielding net power outputs between 0 and 8 kW
and condenser heat transfer rates between 0 and 60 kW.
CTo evaluate the performance of different working fluids in
the studied WHR system, simulations were also performed
with cyclopentane and ethanol as the working fluids. The
results indicated that the evaporating pressures and
expander inlet temperatures for these fluids were similar to
those of water, but that they had higher mass flows in the
cycle. The increased mass flows were a result of the lower
latent heat and a better thermal match with the heat source,
allowing for more heat transfer between source and cycle.
Because of the higher flows and expander efficiencies,
cyclopentane and ethanol outperformed water, providing
net power outputs between 1.8 and 9.6 kW and 1.0 and
7.8 kW, respectively.
CThe steady-state results for the three working fluids were
used to simulate the performance over a typical driving cycle
of a long haul truck. Although transient effects were not
taken into account and the expander speed was not
controlled by the engine speed (as would be the case in a real
system due to the mechanical coupling), the results still
allow for a comparison between the thermodynamic per-
formance of the systems with the different working fluids.
The total recovered energy during the driving cycle was 11.2,
8.2, and 5.2 MJ for cyclopentane, ethanol, and water,
respectively, corresponding to recoveries of 3.4, 2.5, and 1.6%
relative to the total energy requirement of the engine.
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
Acknowledgments
This research was made possible by funding provided by the
Strategic Vehicle Research and Innovation Programme (FFI) of the
Swedish Energy Agency. The authors would like to thank the
partners in the WHR project: Gnutti Carlo, IAV, Lund University,
Scania, TitanX, Volvo Cars, and Volvo Group.
Nomenclature
Aarea (m
2
)
C
d
discharge coefficient ()
hspecific enthalpy (J/kg)
MW molecular weight (kg/kmol)
_
mmass flow rate (kg/s)
Nrotational speed (rpm)
ppressure (Pa)
_
Qheat transfer rate (W)
sentropy (J/kg/K)
ttime (s)
Ttemperature (K)
Vvolume (m
3
)
_
Vvolume flow rate (m
3
/s)
_
Wpower (W)
Greek symbols
h
efficiency ()
εeffectiveness ()
4
f
filling factor ()
r
density (kg/m
3
)
t
torque (Nm)
Subscripts
amb ambient
bpv bypass valve
cond condenser
cool coolant
corr correction
crit critical
Subscripts (continued)
el electrical
eng engine
evap evaporator
exh exhaust
J. Rijpkema, O. Erlandsson, S.B. Andersson et al. Energy 238 (2022) 121698
15

exp expander
is isentropic
mech mechanical
pmp pump
sh shaft
sub subcooled
sup superheated
th theoretical/thermodynamic
Abbreviations
CAC
charge air cooler
BPV
bypass valve
EGR
exhaust gas recirculation
EGRC
exhaust gas recirculation cooler
ESC
European stationary cycle
HD
heavy-duty
HDD
heavy-duty Diesel
HW
highway
GHG
greenhouse gas
GWP
global warming potential
ODP
ozone depletion potential
ORC
organic Rankine cycle
SV
safety valve
WHR
waste heat recovery
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